• Journal of Advanced Navigation Technology
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• v.13 no.1
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• pp.142-150
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• 2009

It is very important to generate a simplified model from a complex 3D character in computer game. We propose a new method of extracting feature lines from a 3D game character. Given an unstructured 3D character model containing texture information, we use model feature map (MFM), which is a 2D map that abstracts the variation of texture and curvature in the 3D character model. The MFM is created from both a texture map and a curvature map, which are produced separately by edge-detection to locate line features. The MFM can be edited interactively using standard image-processing tools. We demonstrate the technique on several data sets, including, but not limited to facial character.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.923-951
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• 2024

We consider a vector bundle map F : E₁ → E₂ between Lie algebroids E₁ and E₂ over arbitrary bases M₁ and M₂. We associate to it different notions of curvature which we call A-curvature, Q-curvature, P-curvature, and S-curvature using the different characterizations of Lie algebroid structure, namely Lie algebroid, Q-manifold, Poisson and Schouten structures. We will see that these curvatures generalize the ordinary notion of curvature defined for a vector bundle, and we will prove that these curvatures are equivalent, in the sense that F is a morphism of Lie algebroids if and only if one (and hence all) of these curvatures is null. In particular we get as a corollary that F is a morphism of Lie algebroids if and only if the corresponding map is a morphism of Poisson manifolds (resp. Schouten supermanifolds).

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.379-396
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• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1461-1466
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• 2010

aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.05a
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• pp.731-734
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• 2007

본 연구는 구조광 기반의 깊이 에지를 이용하여 조명의 변화와 복잡한 배경에 상관없이 손 제스처의 외곽선 영상을 안정적으로 획득하였고, 제스처 영상을 표현하기 위하여 Curvature Scale Space(CSS) map을 이용하였다. 기존의 CSS map은 외곽선 영상의 깊은 굴곡과 완만한 굴곡을 잘 구분하지 못하는 문제점이 있었으나, 본 연구에서는 이러한 문제점을 분석하고, 이를 개선하기 위해서 각도 좌표를 이용한 CSS map 생성 방법을 제안하였다. 실험을 통해서 제안한 방법이 기존의 CSS map보다 우수한 인식 성능이 있음을 보였다.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.789-796
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• 1996

A complete open manifold with nonnegative curvature is diffeomorphic to the normal bundle of the soul, and the projection map is a Riemannian submersion. Under certain circumstances, we prove that a harmonic map from a compact manifold followed by the projection is again harmonic. Therefore we obtain a harmonic map onto the soul when there is a harmonic map into an open manifold.

• Journal of Multimedia Information System
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• v.4 no.4
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• pp.249-254
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• 2017

Digital vector maps must be compressed effectively for transmission or storage in Web GIS (geographic information system) and mobile GIS applications. This paper presents a polyline compression method that consists of polyline feature-based hybrid simplification and second derivative-based data compression. Experimental results verify that our method has higher simplification and compression efficiency than conventional methods and produces good quality compressed maps.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.43-53
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• 2021

We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.